Topological degree for some parabolic equations with Riemann-Liouville time-fractional derivatives

This work tackles a class of nonlinear parabolic equations in divergence form having fractional time order derivatives. We consider parabolic equations involving second-order spacial operators with Riemann-Liouville time-fractional derivatives. We establish the existence and uniqueness of weak solutions to the studied models. Our theoretical approach relies essentially on the use of Leray-Schauder topological degree and involves some new technical estimates.